Wright, 25, started 11 games for the White Sox this season, going 0-4 with a 5.93 ERA before getting demoted on June 11. Wright is scheduled to start Saturday night's game against the Mariners.
The 34-year-old White questioned Manuel last week in regards to his handling of the bullpen, claiming Manuel has overworked some while over-resting others. In 34 games, White posted a 6.61 ERA in 47 2/3 innings, going 1-2.